Experimentally, in moiré + monolayer system, we expect \(J_t\)  to be larger than \(J_b\)  and \(J_p\)  because the top layer is less correlated. Then according to our analysis above it is easy to reach the paired superfluid phase with a spin gap \(\Delta _t>0\)  in the top layer. As long as there is a small \(J^\prime _b\sim 0.1 J_b\)  in the bottom layer, we can realize either the Z\(_2\)  SL I + PSF phase or the Z\(_2\)  SL II + PSF phases. These phases have spin gapes in both layers and have preformed cooper pairs, the same as the resonating-valence-bond (RVB) state first proposed for high Tc cuprates[1]}. Therefore it is very interesting to search for possible superconductivity by doping the bilayer Mott insulator with the \(Z_2\)  spin liquids orders.
